Quote:
An aquarium contains a variety of tropical fish. Is the ratio of the number of reef stonefish to the number of tetra fish in the aquarium
greater than 1 to 22?
1) The number of tetra fish in the aquarium is less than 40 greater than the number of reef stonefish in the aquarium.
2) If 2 new reef stonefish were added to the aquarium, the ratio of the number of reef stonefish to the number of tetra fish in the aquarium would be greater than 1 to 11.
Hmmm, okay, reading the question, I do notice that a '1 to 22' ratio is a pretty decent spread for the GMAT.
Statement 1 tells me the different is <40. Well... I could have 1 reef and 2 tetra, and that's a 1:2 ratio, so the answer would be yes. Or I could have 1 reef and 23 tetra, and that's a 1:23 ratio, so the answer would be no. Both cases have a difference of less than 40.
Eliminate A/D
Statement 2 says that if 2 reef are added, the ratio would be > 1:11.
So this means (R+2)/S > 1/11
Which means 11R + 22 > S
Which means S - 11R < 22...
Hmmm, So R could be 2 and S could be 23 (and 2:23 > 1:22, so the answer would be 'yes')
Or r could be 1 and S could be 30, and 1:30 < 1:22, so the answer could be 'no.'
Eliminate B.
Honestly at this point I've spent enough time and I would guess. In general, I err sufficient, especially when a question seems kind of complicated and tedious, so I'd guess 'C'.
Now, I'll figure out if that is correct...
And I realize, D'oh, the cases I tested for statement 2 were perfectly consistent with statement 1--the difference in fish was <40 for both cases in statement 2. So the answer must be E. So I missed it. Oh well. This doesn't mean 'err sufficient' isn't still the better advice, BUT, there is a takeaway here I should remind myself of:
Check to see if the cases you use in one statement are applicable cases in the other statement (or can be easily 'tweaked'). It's probably also good advice, if I decide I need to guess between C and E as I did here, to just check if my statements already fit both statements. While I was running long and needed to guess, the extra 10 seconds of care would have gotten a right answer instead of a wrong answer.